Model-categorical

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Idea

There are several contexts in which it is of relevance that a certain property of a morphismf:A→Bf : A \to B is preserved (or stable) under pullback, i.e. also shared by the the morphism f˜:X×BA→X\tilde{f}: X \times_B A \to X for any pullback diagram

Similarly, the property of being right orthogonal to a class of morphisms is stable under pullback. Thus, the right class in any orthogonal factorization system is stable under pullback. If the left class is also pullback-stable, the OFS is called stable.